The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl2)

Received July 19, 2011, in final form October 10, 2011; Published online October 25, 2011; Misprint in Lemma 7.1 is corrected March 16, 2012

Abstract(this is shortened html-version of the paper's abstract)
Around 1992 A. Zhedanov introduced the Askey-Wilson algebra
AW(3). Recently we introduced a central extension Δ of AW(3)
called the universal Askey-Wilson algebra. In this
paper we discuss a connection between
Δ and the quantum algebra Uq(sl2).
Our main result is an
algebra injection from Δ into
a relative of
Uq(sl2);
the relative is obtained
from
Uq(sl2)
by adjoining three mutually
commuting indeterminates. We describe the
injection using the equitable presentation
of Uq(sl2).